高等数学英文1-2-10.ppt

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1、Chapter1FunctionsandLimits1.2FunctionsI.Functions1.DefinitionAfunctionfisaruleofcorrespondencethatassociateswitheachobjectxinonesetandasinglevalueyfromasecondset.DomainRangeindependentvariabledependentvariablefQ:howtofindthedomainofafunction?Q:howtodiscriminatetw

2、ofunctionsarethesame?Findthecircumferenceofapolygonwithnequalsidesthatisinscribedtoacirclewithradiusr.I.Functions1.Definition2.SpecialFunctionsGreatestintegerfunction=thegreatestintegerlessthanorequaltox.xoySignfunctionxoyI.FunctionsII.PropertiesofFunctions1.Bound

3、ednessDef:Wesayf(x)isboundedabove(below)onXifyxoMNII.PropertiesofFunctions1.BoundednessDef:Wesayf(x)isboundedabove(below)onXifWesayf(x)isboundedonXif-MyxoMN2.MonotonicitythenfisincreasingonXiffisdecreasingonXifDef:Forexample,II.PropertiesofFunctionsII.Propertiesof

4、Functions3.OddandevenfunctionsForexample,4.PeriodicfunctionsDef:wesayf(x)isaperiodicfunctionifDef:LetDbesymmetrictotheorigin.Wesayf(x)isanevenfunctionifWesayf(x)isanoddfunctionifIII.InverseFunctionsThegraphsoffandaresymmetricwithliney=x.Iffisamonotonicfunction,the

5、nsoisIV.CompositeFunctionsiscalledthecompositionoffwithg.Restriction:isinthedomainoff,thatisForexample:V.ElementaryFunctions1.BasicElementaryFunctionsPowerFunctionV.ElementaryFunctions1.BasicElementaryFunctionsExponentialFunctionV.ElementaryFunctions1.BasicElement

6、aryFunctionsLogarithmicFunctionV.ElementaryFunctions1.BasicElementaryFunctionsTrigonometricFunctionsV.ElementaryFunctions1.BasicElementaryFunctionsTrigonometricFunctionsV.ElementaryFunctions1.BasicElementaryFunctionsTrigonometricFunctionsV.ElementaryFunctions1.Bas

7、icElementaryFunctionsInverseTrigonometricFunctionsV.ElementaryFunctions1.BasicElementaryFunctionsInverseTrigonometricFunctionsV.ElementaryFunctions2.ElementaryFunctionsDef:Acompositefunctionthatisobtainedfromoperationsonorcomposedbybasicelementaryfunctions.Forexam

8、ple:ClassexercisesSketchthegraphsofandusingthesamecoordinateaxes.Thensketchbyaddingordinates.Sketchthegraphof1.2.